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Home of the Submariner jumper. Shop the range of North Sea Clothing 100% British Wool knitwear. Knitted and hand linked in Scotland.
Obviously not cashmere like the OP asked about, and much thicker than 4-ply ... but for me, wonderful. On the other hand, if the OP wants a turtleneck for wearing under a sportscoat or suit jacket, then Northsea won't really be the best choice.
I wonder if the OP would consider expanding his search to high-quality merino as well? Just a thought. (Much of the less expensive cashmere out there is of suspect quality, with shorter hairs that keep the initial softness one expects but the fabric very quickly succumbs to pilling. Equally priced merino is far more satisfactory in performance, even if not as super-soft.)